WO2021246497A1 - Shape measurement system and shape measurement method - Google Patents

Abstract

The purpose of the present invention is to provide a shape measurement system and a shape measurement method whereby the three-dimensional shape of a linear object to be measured can be derived over a long distance and with high resolution.　The shape measurement system according to the present invention comprises: a multicore optical fiber 10 having a center core 11 positioned in the center of the cross section thereof and three or more outer peripheral cores 12 positioned at equal intervals concentrically with respect to and outside of the center core 11; a measurement device 20 for measuring the backward Brillouin scattered light distribution in the propagation direction of each core of the multicore optical fiber 10; and an analysis device 30 for calculating position coordinates, in three-dimensional space, of a linear structure having an unknown three-dimensional shape from the backward Brillouin scattered light distributions of a multicore optical fiber 10 positioned along the linear structure having an unknown three-dimensional shape and a multicore optical fiber positioned along a linear structure having a known three-dimensional shape.

Description

Shape measurement system and shape measurement method

The present disclosure relates to an apparatus and a method for deriving a three-dimensional shape of an object to be measured, such as a pipeline or a submarine cable, by a reflectometry technique using an optical fiber.

A technique has been proposed in which the reflection spectrum in the frequency domain of each core of a multi-core optical fiber is measured and analyzed by OFDR (Optical Frequency Domain Reflectometry) to derive a three-dimensional shape to be measured (for example, Non-Patent Document 1). reference.). Further, a method of imparting FBG (Fiber Bragg Grating) to the entire length of the sensing medium (optical fiber) to improve the measurement resolution has also been proposed (see, for example, Non-Patent Document 2).

When trying to derive the three-dimensional shape of the object to be measured by OFDR, the following difficulties occur.
(1) OFDR can realize high resolution on the order of several tens of mm, but the measurement distance is limited to about several tens of meters, and it is difficult to derive a long-distance three-dimensional shape.
(2) If an FBG is added to an optical fiber, it becomes difficult to improve the ease of manufacturing and the economic efficiency of the optical fiber.
(3) The technique of performing shape identification by quasi-distribution measurement such as addition of FBG has a limitation on the number of measurement points, and it is difficult to identify the shape over a long distance.
(4) In the case where the optical fiber to which the FBG is applied is embedded in the object to be measured of the non-linear material, the center frequency of the reflection by the FBG changes due to the temperature and stress, and the distortion and curvature of the optical fiber to be measured also have non-linearity. Therefore, it is difficult to identify the shape change of the object to be measured.

Therefore, an object of the present invention is to provide a shape measurement system and a shape measurement method capable of deriving a three-dimensional shape of a linear object to be measured over a long distance and with high resolution in order to solve the above problems. do.

In order to achieve the above object, the shape measurement system according to the present invention uses a multi-core optical fiber having a predetermined core arrangement as a sensing medium, and analyzes data acquired by BOTDR (Brillouin Optical Time Domain Reflectometer). ..

Specifically, the shape measuring system according to the present invention is
A central core arranged in the center of the cross section, and a multi-core optical fiber having three or more outer peripheral cores arranged concentrically and outside the central core at equal intervals.
A measuring device for measuring the rear Brillouin scattered light distribution in the propagation direction of each core of the multi-core optical fiber, and a measuring device.
The rear Brilluan scattered light distribution of the multi-core optical fiber arranged along a linear structure having an unknown three-dimensional shape and the multi-core optical fiber arranged along a linear structure having a known three-dimensional shape. From the analysis device that calculates the position coordinates in the three-dimensional space of the linear structure whose three-dimensional shape is unknown and identifies the time change.
To prepare for.

Further, the shape measuring method according to the present invention is
A central core arranged in the center of the cross section and a multi-core optical fiber having 3 or more and 6 or less outer peripheral cores arranged outside the central core and concentrically at equal intervals are arranged along the linear structure. matter,
The rear Brilluan scattered light distribution in the propagation direction of each core of the multi-core optical fiber is measured, and the multi-core optical fiber and the three-dimensional shape arranged along the linear structure whose three-dimensional shape is unknown are known. From the rear Brilluan scattered light distribution of the multi-core optical fiber arranged along a certain linear structure, the position coordinates in the three-dimensional space of the linear structure whose three-dimensional shape is unknown are calculated, and the time change thereof is calculated. To identify,
I do.

Long-distance measurement is possible by measuring the rear Brillouin scattered light for each core of the multi-core optical fiber. Further, by maintaining the distance between the center core of the multi-core optical fiber and the outer peripheral core and the distance between the adjacent outer peripheral cores, it is possible to detect minute fluctuations in the object to be measured. Therefore, the present invention can provide a shape measurement system and a shape measurement method capable of deriving a three-dimensional shape of a linear object to be measured over a long distance and with high resolution.

The specific analysis method is as follows.
Let z be the position in the longitudinal direction of the multi-core optical fiber.
The analyzer is
The amount of strain at the position z of each core of the multi-core optical fiber obtained from the rear Brillouin scattered light distribution when the multi-core optical fiber is arranged along a linear structure whose three-dimensional shape is unknown, and the above-mentioned The difference from the strain amount of the position z of each core of the multi-core optical fiber obtained from the rear Brillouin scattered light distribution when the multi-core optical fiber is arranged along a linear structure whose three-dimensional shape is known. Calculating the differential distortion at a certain position z,
To calculate the bending strain ε of each of the outer peripheral cores by subtracting the differential strain of the central core from the differential strain of each of the outer peripheral cores.
Using the relational expression (1), the curvature κ and the bending angle β at the position z of the multi-core optical fiber are calculated from the bending strain ε for each outer core, and the bending angle β is differentiated by the arc length to calculate the torsion of a curve. Using the Frenet-Serret formula, the position coordinates in the three-dimensional space of the linear structure whose three-dimensional shape is unknown are calculated from the curvature κ and the torsion at the position z, and the time change is identified. matter,
It is characterized by doing.
The bending angle β represents an angle formed by a vector connecting the MCF center and the center of curvature and a reference direction vector, for example, a vector connecting the MCF center and a specific core in the MCF cross section.
[Relational formula (1)]
ε ＝ r ・ κ ・ cos (α-β)
However, r is the distance between the centers of the central core and the outer peripheral core, and α is an angle representing the position of the outer peripheral core in the cross section of the multi-core optical fiber.

In this method, when a multi-core optical fiber is placed along a structure, an unintended twist may occur, which may cause an error in the measurement result. In such a case
The multi-core optical fiber is given a known torsion, and the analyzer is known to have a torsional strain occurring in the multi-core optical fiber when calculating the position coordinates. The unintended torsion that occurs when the three-dimensional shape is placed along a linear structure whose three-dimensional shape is unknown is estimated based on the strain due to the torsion, and the influence of the unintended torsion is excluded. matter,
Is preferable.

The specific analysis method in this case is as follows.
Let z be the position in the longitudinal direction of the multi-core optical fiber.
The analyzer is
The amount of strain at the position z of each core of the multi-core optical fiber obtained from the rear Brillouin scattered light distribution when the multi-core optical fiber is arranged along a linear structure whose three-dimensional shape is unknown, and the above-mentioned The difference from the strain amount of the position z of each core of the multi-core optical fiber obtained from the rear Brillouin scattered light distribution when the multi-core optical fiber is arranged along a linear structure whose three-dimensional shape is known. Calculating the differential distortion at a certain position z,
To calculate _{the bending strain ε bending, i} of each of the outer peripheral cores by subtracting the differential strain of the central core from the differential strain of each of the outer peripheral cores.
Using the relational expression (2) excluding the influence of the unintended twist, the curvature κ and the bending angle β at the position z of the multi-core optical fiber are calculated from the _{bending strain ε bending, i for each outer core.} , And, using the Frenet-Serret formula, calculate the position coordinates in the three-dimensional space of the linear structure whose three-dimensional shape is unknown from the curvature κ at the position z and the bending angle β.
It is characterized by doing.

However, r is the distance between the centers of the central core and the outer peripheral core, k ₁ is the twist correction coefficient represented by the equation (3), ν is the Poisson's ratio of the multi-core optical fiber, and a _i is the core i. The initial angle of, ω _i is the angle representing the position of the outer peripheral core in the cross section at the position z of the multi-core optical fiber represented by the equation (4), p is the spin rate of the outer peripheral core, and ε _twisting is the multi-core light. The torsional strain generated at the position z of the fiber, φ (z) is the specific torsion angle at the position z of the multi-core optical fiber represented by the equation (5), and k ₂ is the equation (6). It is a correction coefficient of twist represented by.

In this case, it is preferable that the analyzer calculates the spin rate p of the outer peripheral core from the periodic fluctuations _{of the bending strain ε bending and i of each of the outer peripheral cores.} The error in the number of twists can be taken into consideration due to the manufacturing error of the multi-core optical fiber, and the shape change of the object to be measured can be specified with high accuracy.

The multi-core optical fiber preferably has 3 or more outer peripheral cores and a clad diameter of 375 μm or more.
Further, in the multi-core optical fiber, the distance between the center core and the outer peripheral core is preferably 120 μm or more.
Fan-in / fan-out (FIFO) devices can be easily realized by bundling existing single-mode fibers (clad diameter 125 μm). Further, the wider the distance between the center of the central core and the center of the outer peripheral core, the larger the distortion generated in the outer peripheral core, and the higher the dynamic range can be achieved.

The above inventions can be combined as much as possible.

The present invention can provide a shape measurement system and a shape measurement method capable of deriving a three-dimensional shape of a linear object to be measured over a long distance and with high resolution.

It is a figure explaining the structure of the shape measurement system which concerns on this invention. It is a figure explaining the cross section of the multi-core optical fiber of the shape measurement system which concerns on this invention. It is a figure explaining the effect of the shape measurement system which concerns on this invention. It is a figure explaining the shape measuring method which concerns on this invention. It is a figure explaining the shape measuring method which concerns on this invention. It is a figure explaining the measurement example in the shape measuring system which concerns on this invention. It is a figure explaining the measurement example in the shape measuring system which concerns on this invention. It is a figure explaining the multi-core optical fiber provided in the shape measuring system which concerns on this invention. It is a figure explaining the shape measuring method which concerns on this invention. It is a figure explaining the multi-core optical fiber provided in the shape measuring system which concerns on this invention. It is a figure explaining the specific twist angle of a multi-core optical fiber. It is a figure explaining the spin rate measurement method of a multi-core optical fiber.

An embodiment of the present invention will be described with reference to the accompanying drawings. The embodiments described below are examples of the present invention, and the present invention is not limited to the following embodiments. In addition, the components having the same reference numerals in the present specification and the drawings shall indicate the same components.

[Embodiment 1]
FIG. 1 is a diagram illustrating a shape measuring system of the present embodiment. This shape measurement system is
A central core 11 arranged in the center of the cross section, and a multi-core optical fiber 10 having three or more outer peripheral cores 12 arranged concentrically and outside the central core 11 at equal intervals.
A measuring device 20 for measuring the rear Brillouin scattered light distribution in the propagation direction of each core of the multi-core optical fiber 10 and a measuring device 20.
The rear Brillouin scattered light distribution of the multi-core optical fiber 10 arranged along a linear structure whose three-dimensional shape is unknown and the multi-core optical fiber 10 arranged along a linear structure whose three-dimensional shape is known. The analysis device 30 that calculates the position coordinates in the three-dimensional space of the linear structure whose three-dimensional shape is unknown from the above and identifies the time change thereof.
To prepare for.
Note that FIG. 1 shows an example in which a specific one core of the multi-core optical fiber 10 and a measuring device 20 for measuring the rear Brillouin scattered light distribution are connected. As another configuration, a fan-out mechanism that separates each core of the multi-core optical fiber into a single-core optical fiber, and a form in which the multi-core optical fiber 10 and the measuring device 20 are connected via an optical switch may be used.

This shape measurement system uses a multi-core optical fiber 10 as a sensing medium, a measuring device (BOTDR) 20 for detecting rear Brillouin scattered light in the propagation direction of each core of the multi-core optical fiber 10, and measurement data acquired by the BOTDR 12. It is provided with an analysis device 30 for analysis.

The multi-core optical fiber 10 is installed along the longitudinal direction of the linear structure to be measured. The linear structure is, for example, a pipeline, a riser (a pipe through which a fluid can pass from the seabed to equipment on the sea surface in offshore drilling and offshore production), a submarine cable, and the like. FIG. 2 is a diagram illustrating a cross section of the multi-core optical fiber 10. The multi-core optical fiber 10 has a central core in the center of the cross section and an outer peripheral core arranged at substantially equal intervals on the same circumference from the center of the cross section, for a total of four cores. In the present embodiment, the four cores have substantially the same refractive index distribution and optical characteristics, but the structure may be arranged so that the refractive index distributions and optical characteristics of the cores are intentionally different. ..

The limits on the number of cores are as follows. If the number of cores is 3 or less (2 or less outer peripheral cores), the shape cannot be identified. On the other hand, when the number of cores is 5 or more (4 or more outer peripheral cores), the measurement accuracy is improved, but the measurement time is increased by the number of cores.
Also, a circle of a certain radius can be surrounded by six circles of the same radius in contact with it. In this case, the total number of circles is seven. That is, a single-core optical fiber having the same diameter can be used as a multi-core optical fiber at the core position when seven optical fibers are closely arranged, and a FIFO can be easily produced.
On the other hand, when the number of outer circles is 7 or more (the total number of circles is 8 or more), if 7 or more circles are placed around one circle, a gap will be created between the center circle and the outer circle. to be born. That is, eight or more single-core optical fibers having the same diameter cannot be arranged in the densest position, the clad diameter of the multi-core optical fiber becomes large, and it becomes difficult to create a fan-in / fan-out (FIFO).
Therefore, it is desirable that the number of outer peripheral cores of the multi-core optical fiber is 3 or more and 6 or less.

The multi-core optical fiber 10 has a larger clad outer diameter (> 125 μm) than a general communication optical fiber. The distance between the center core 11 arranged at the center of the optical fiber and the outer peripheral core 12 arranged on the outer periphery of the central core 11 is set to be larger than 30 μm. The reason is that in a standard multi-core optical fiber having a clad outer diameter of 125 μm, the distance between the center core and the outer peripheral core that can be arranged while suppressing the influence of leakage loss is about 30 μm.

FIG. 3 is a diagram for explaining the relationship between the center-to-center distance and the strain amount of the outer peripheral core 12 with respect to the curvature of the center of the multi-core optical fiber 10 in which (α-β) is 0 in the relational expression (1). From FIG. 3, the amount of strain obtained by a standard multi-core optical fiber having a clad outer diameter of 125 μm even when the distance between the centers of the central core 11 and the outer peripheral core 12 is 120 μm or more and the curvature is κ = 0.5 [1 / m]. It can be seen that a strain amount of 5 times or more can be obtained. This means that by increasing the distance between the centers of the central core 11 and the outer peripheral core 12, the sensitivity to the shape change of the small curvature generated in the multi-core optical fiber 10 can be improved.

As described above, a FIFO device can be easily realized by bundling an existing single-mode fiber (clad diameter 125 μm), and a central core of a multi-core optical fiber 10 can be used by using a FIFO made of an existing single-mode fiber. Since the distance between the center of the 11 and the outer peripheral core 12 is 125 μm and sufficient sensitivity can be obtained even for a small shape change, in the present embodiment, the clad outer diameter of the multi-core optical fiber 10 is 375 μm (= 125 μm × 3). ) Was examined.

Next, a shape measuring method for measuring a shape change of an object to be measured by using a multi-core optical fiber 10 will be described with reference to FIG. This shape measurement method is
Arranging the multi-core optical fiber 10 along the linear structure (step S01),
Measuring the rear Brilluan scattered light distribution in the propagation direction of each core of the multi-core optical fiber 10 (step S02), and the multi-core optical fiber 10 and three-dimensionally arranged along a linear structure whose three-dimensional shape is unknown. From the rear Brilluan scattered light distribution of the multi-core optical fiber 10 arranged along the linear structure whose shape is known, the position coordinates in the three-dimensional space of the linear structure whose three-dimensional shape is unknown are calculated and changed over time. (Step S03),
I do. The measuring device 20 performs step S02, and the analysis device 30 performs step S03. In step S02, it is desirable to correct the temperature dependence of the Brilluan frequency shift.

Let z be the position in the longitudinal direction of the multi-core optical fiber 10 from the measuring device 20, which will be described in more detail with respect to step S03.
In step S03
The amount of strain at the position z of each core of the multi-core optical fiber obtained from the rear Brillouin scattered light distribution when the multi-core optical fiber is arranged along a linear structure whose three-dimensional shape is unknown, and the above 3 It is a difference from the strain amount of the position z of each core of the multi-core optical fiber obtained from the rear Brillouin scattered light distribution when the multi-core optical fiber is arranged along a linear structure whose dimensional shape is known. Calculating the differential strain at position z (step S31),
The bending strain ε of each of the outer peripheral cores is calculated by subtracting the differential strain of the central core from the differential strain of each of the outer peripheral cores (step S32).
Using the relational expression (1), the curvature κ and the bending angle β at the position z of the multi-core optical fiber are calculated from the bending strain ε for each outer core (step S33), and the bending angle β is differentiated by the arc length. And using the Frenet-Serret formula, calculate the position coordinates in the 3D space of the linear structure whose 3D shape is unknown from the curvature κ and the torsion at the position z, and time. Identifying changes (step S34),
I do.

FIG. 5 is a diagram illustrating a specific procedure when measuring a linear structure whose three-dimensional shape is unknown by this shape measuring method.
[Step A]
First, the multi-core optical fiber 10 is laid along a linear structure whose three-dimensional shape is known (for example, a water pipe that has already been laid), and the rear Brillouin scattered light of each core in a steady state (reference state). Get the distribution characteristics of. This is used as the reference data.
[Step B]
Next, in a state where the three-dimensional shape of the linear structure has changed (for example, a water pipe that is expected to be deformed due to an earthquake or the like), the distribution characteristics of the rear Brillouin scattered light of each core are acquired again. This is used as comparison data.
[Step C]
Next, the difference between the comparison data and the reference data is calculated for each core and each position z to derive the difference strain.
[Step D]
Next, the differential strain of the central core is subtracted from the differential strain of each outer peripheral core, and the bending strain ε at the position z is derived for each outer peripheral core.
[Step E]
Substitute the ε derived by Step D into the relational expression (1) between the bending strain ε of the outer peripheral core, the curvature κ of the multi-core optical fiber 10 and the bending angle β.
[Relational formula (1)]
ε ＝ r ・ κ ・ cos (α-β)
However, r is the distance between the centers of the central core 11 and the outer peripheral core 12, and α is an angle representing the position of the outer peripheral core 12 in the cross section of the multi-core optical fiber 10. For example, r is 125 μm and α is 0 °, 120 °, and 240 ° for each outer core.
In this embodiment, since there are three outer cores, a ternary simultaneous equation can be obtained. From this equation, the curvature κ and the bending angle β at the position z are calculated. Here, the bending strain ε differs for each core, but since the curvature κ and the bending angle β are the same in all cores, the curvature κ and the bending angle β at the position z are determined by the least squares method.
[Step F]
Using the Frenet-Serret formula, the position vector (three-dimensional shape) of the multi-core optical fiber 10 is determined from the curvature κ and the bending angle β for each distance z determined by Step E. In addition, in order to improve the position accuracy, it is preferable to correct the three-dimensional shape by using a known end point.

(Example 1)
FIG. 6 is a diagram illustrating a first example in which the three-dimensional shape of the multi-core optical fiber 10 is measured by the shape measuring method. In FIGS. 6A to 6E, the longitudinal distance (position z described above) of the multi-core optical fiber 10 is represented by s [m]. In FIG. 6 (f), the three-dimensional space in which the multi-core optical fiber 10 is arranged is represented by the x-axis, the y-axis, and the z-axis. Note that the z-axis here is different from the position z described above.

In this embodiment, the reference data of Step A in FIG. 5 was acquired in a state where the multi-core optical fiber 10 for sensing was linearly stretched. Next, the vicinity of the center of the multi-core optical fiber 10 was rotated clockwise with a constant curvature, and the comparison data of Step B in FIG. 5 was acquired. 6 (a), (b), and (c) are the results of the reference data of Step A, the comparison data of Step B, and the difference distortion of Step C, respectively. The dotted line, broken line, and alternate long and short dash line in the figure indicate the difference between the outer peripheral cores. 6 (d) and 6 (e) show the evaluation results of the curvature κ and the angle β of the multi-core optical fiber 10, respectively. FIG. 6F shows the spatial coordinates of the multi-core optical fiber 10 in consideration of the position vector, and the curvature given to the vicinity of the center of the multi-core optical fiber 10 can be detected with high accuracy.

(Example 2)
FIG. 7 is a diagram illustrating a second example in which the three-dimensional shape of the multi-core optical fiber 10 is measured by the shape measuring method. Also in FIGS. 7A to 7E, the distance in the longitudinal direction of the multi-core optical fiber 10 (position z described above) is represented by s [m]. Also in FIG. 7 (f), the three-dimensional space in which the multi-core optical fiber 10 is arranged is represented by the x-axis, the y-axis, and the z-axis. Note that the z-axis here is different from the position z described above.

In this embodiment, the reference data of Step A in FIG. 5 was acquired in a state where the multi-core optical fiber 10 for sensing was linearly stretched. Next, the vicinity of the center of the multi-core optical fiber 10 was rotated counterclockwise with a constant curvature, and the comparison data of Step B in FIG. 5 was acquired. 7 (a), (b), and (c) are the results of the reference data of Step A, the comparison data of Step B, and the difference distortion of Step C, respectively. The dotted line, broken line, and alternate long and short dash line in the figure indicate the difference between the outer peripheral cores. 7 (d) and 7 (e) show the evaluation results of the curvature κ and the angle β of the multi-core optical fiber 10, respectively. FIG. 7 (f) shows the spatial coordinates of the multi-core optical fiber 10 in consideration of the position vector, and the shape change in the direction opposite to that of FIG. 6 (f) (counterclockwise) can be detected with high accuracy.

[Embodiment 2]
When a multi-core optical fiber is placed along a linear structure as a sensing medium, an unintended twist may occur and an error may occur in the measurement result. Therefore, in the present embodiment, it is decided to intentionally twist the multi-core optical fiber used for the sensing medium. When identifying the shape of a linear structure, the strain due to unintended torsion below the torsional strain can be eliminated by calculation, and the accuracy of shape identification can be improved.

The system configuration of the shape measurement system of the present embodiment is different from the system configuration of the shape measurement system described in FIG. 1 in that the multi-core optical fiber 10 is given a known twist and the analysis procedure of the analysis device 30 is different. ..

FIG. 8 is a diagram illustrating a multi-core optical fiber 10. FIG. 8A describes bending strain measured by the multi-core optical fiber 10 in a twisted state, and FIG. 8B describes bending strain measured by the multi-core optical fiber 10 in a twisted state. The core 0 is the central core, and the cores 1 to 3 are the outer peripheral cores.
If there is no bending strain, the bending strain becomes zero and overlaps in all cores regardless of the presence or absence of twisting. In addition, the bending strain of the central core is zero regardless of the presence or absence of twisting. In the case of the multi-core optical fiber 10 without twisting, the bending strain measured when a bending with a constant curvature is applied is as shown between the axial position z = 2m and z = 12m in FIG. 8 (A). Although the amount of strain differs for each core, a certain amount of strain is observed.
Further, FIG. 8B describes the bending strain of the multi-core optical fiber 10 in which a twist is applied between the axial positions z = 2 m and z = 12 m. In FIG. 8 (B), bending with a constant curvature is applied as in FIG. 8 (A), but in the section where bending is applied, the positions of the outer peripheral cores are exchanged by twisting, so that the amount of strain is positive or negative. Can be confirmed to be inverted. When the multi-core optical fiber 10 is arranged in a linear structure as a sensing medium, twisting is required in all the sections arranged in the linear structure.

The analyzer 30 has a linear structure whose three-dimensional shape is unknown based on the torsional strain generated in the multi-core optical fiber 10 and the known torsional strain when calculating the position coordinates. Estimate the unintended twist that occurs when arranging along an object, and exclude the effects of the unintended twist.

In this shape measuring method, step S33 described in the shape measuring method of FIG. 4 is different from the description of the first embodiment. That is, in step S03,
The amount of strain at the position z of each core of the multi-core optical fiber obtained from the rear Brillouin scattered light distribution when the multi-core optical fiber is arranged along a linear structure whose three-dimensional shape is unknown, and the above-mentioned The difference from the strain amount of the position z of each core of the multi-core optical fiber obtained from the rear Brillouin scattered light distribution when the multi-core optical fiber is arranged along a linear structure whose three-dimensional shape is known. Calculating the differential strain at a certain position z (step S31),
_{The bending strain ε bending, i} of each of the outer peripheral cores is calculated by subtracting the differential strain of the central core from the differential strain of each of the outer peripheral cores (step S32).
Using the relational expression (2) excluding the influence of the unintended twist, the curvature κ and the bending angle β at the position z of the multi-core optical fiber are calculated from the _{bending strain ε bending, i for each outer core.} (Step S33), and using the Frenet-Serret formula, calculate the position coordinates in the three-dimensional space of the linear structure whose three-dimensional shape is unknown from the curvature κ and the bending angle β at the position z (step S34). ),
I do.

FIG. 9 is a diagram illustrating a specific procedure when measuring a linear structure whose three-dimensional shape is unknown by this shape measuring method. Here, "i" is a core number. Note that i = 0 is the central core, and i of 1 or more is the outer peripheral core.
[Step A]
First, the multi-core optical fiber 10 is laid along a linear structure whose three-dimensional shape is known (for example, a water pipe that has already been laid), and the rear Brillouin scattered light of each core in a steady state (reference state). Get the distribution characteristics of. This is used as the reference data.
[Step B]
Next, in a state where the three-dimensional shape of the linear structure has changed (for example, a water pipe that is expected to be deformed due to an earthquake or the like), the distribution characteristics of the rear Brillouin scattered light of each core are acquired again. This is used as comparison data.
[Step C]
Next, the difference between the comparison data and the reference data is calculated for each core and each position z to derive the difference strain.
[Step D]
Next, the differential strain of the central core is subtracted from the differential strain of each outer peripheral core, and the strains ε _{mix and i} at the position z are derived for each outer peripheral core (i here is 1 or more).
[Step D-α]
The strains ε _{mix and i} include bending strains ε _{bending and i} and torsional strains ε _twisting (where i is 1 or more). Since the relative positional relationship of the outer peripheral cores does not change, _{the torsional strain ε twisting} at the position z is used as shown in the following equation by utilizing the fact that _{the bending strain ε bending and i of all the outer peripheral cores become zero when added.} Is calculated. max {i} means the maximum core number.

_{The torsional strain ε twisting} calculated by the equation (7) is substituted into the equation (5) to calculate the specific torsion angle φ (z) at the position z. FIG. 11 is an image diagram illustrating the specific twist angle φ. The specific twist angle φ is a twist angle per unit length.

Here, r is the distance from the center to the center of the outer peripheral core in the cross section of the multi-core optical fiber 10. k2 is a torsion correction coefficient and is expressed by the following equation. p is the spin rate (the amount of twist per unit length) of the outer peripheral core, which is a design value or a value obtained by a measurement method described later.

[Step E]
The bending strain ε _{bending, i} of the outer peripheral core i is calculated by _{subtracting the ε twisting} derived by Step D-α from _{the strain ε mix, i} of each outer peripheral core.
Then, the specific twist angle φ (z) calculated in the equation (5) is substituted into the equation (4) to calculate the _{angle ω i representing the position of the outer peripheral core i at the position z.} a _i is the initial angle of the outer peripheral core i.

Further, the bending strain ε _{bending, i of the outer peripheral core i and the angle ω i} derived by the equation (4) are substituted into the relational expression (2) of the curvature κ and the bending angle β of the multi-core optical fiber 10.

However, k ₁ is a twist correction coefficient represented by the equation (3).

Here, ν is the Poisson's ratio of the multi-core optical fiber.
In this embodiment, since there are three outer cores, a ternary simultaneous equation can be obtained. The curvature κ and the bending angle β at the position z are calculated by the relational expression (2). Here, the bending strain ε differs for each core, but since the curvature κ and the bending angle β are the same in all cores, the curvature κ and the bending angle β at the position z are determined by the least squares method.
Note that FIG. 10 is an image diagram illustrating a radius r, a bending direction (curvature κ), and a bending angle β of a multi-core optical fiber having an outer peripheral core of 3. 10 (A) is a view seen from the side surface of the multi-core optical fiber, and FIG. 10 (B) is a cross-sectional view of the multi-core optical fiber.
[Step F]
Using the Frenet-Serret formula, the position vector (three-dimensional shape) of the multi-core optical fiber 10 is determined from the curvature κ and the bending angle β for each distance z determined by Step E. In addition, in order to improve the position accuracy, it is preferable to correct the three-dimensional shape by using a known end point.

(Spin rate measurement method)
Here, a method for actually measuring the spin rate will be described.
FIG. 12 is a diagram showing the results of measuring the strain of each core of the twisted multi-core optical fiber in the z direction. When a multi-core optical fiber is twisted, the number of twists (spin rate) may differ from the design value due to manufacturing errors and the like. Therefore, the strain period fluctuates in each core. Therefore, the number of twists (spin rate) is calculated from the periodic fluctuation of the strain by the RTM (short-time Fourier transform). In step D-α described above, the value of the spin rate p calculated from the measured strain period can be used.

(effect)
The shape measurement system according to the present invention can realize a measurement dynamic range of several km to several tens of km by using rear Brillouin scattered light for shape identification of a linear structure. Further, by setting the distance between the center core of the multi-core optical fiber used for detecting the shape change and the center of the outer peripheral core to 120 μm or more, it is possible to detect a minute change having a curvature of 0.5 [1 / m] or less.

10: Multi-core optical fiber 11: Central core 12: Outer peripheral core 20: Measuring device 30: Analytical device

Claims (14)

1. A central core arranged in the center of the cross section, and a multi-core optical fiber having three or more outer peripheral cores arranged concentrically and outside the central core at equal intervals.
   A measuring device for measuring the rear Brillouin scattered light distribution in the propagation direction of each core of the multi-core optical fiber, and a measuring device.
   The rear Brilluan scattered light distribution of the multi-core optical fiber arranged along a linear structure having an unknown three-dimensional shape and the multi-core optical fiber arranged along a linear structure having a known three-dimensional shape. An analyzer that calculates the position coordinates in the three-dimensional space of the linear structure whose three-dimensional shape is unknown from
   Shape measurement system.
2. Let z be the position in the longitudinal direction of the multi-core optical fiber.
   The analyzer is
   The amount of strain at the position z of each core of the multi-core optical fiber obtained from the rear Brillouin scattered light distribution when the multi-core optical fiber is arranged along a linear structure whose three-dimensional shape is unknown, and the above-mentioned The difference from the strain amount of the position z of each core of the multi-core optical fiber obtained from the rear Brillouin scattered light distribution when the multi-core optical fiber is arranged along a linear structure whose three-dimensional shape is known. Calculating the differential distortion at a certain position z,
   To calculate the bending strain ε of each of the outer peripheral cores by subtracting the differential strain of the central core from the differential strain of each of the outer peripheral cores.
   Using the relational expression (1), calculate the curvature κ and bending angle β at the position z of the multi-core optical fiber from the bending strain ε for each outer core, and using the Frenet-Serret formula, the curvature at the position z. To calculate the position coordinates in the three-dimensional space of the linear structure whose three-dimensional shape is unknown from κ and the bending angle β.
   The shape measuring system according to claim 1.
   [Relational formula (1)]
   ε ＝ r ・ κ ・ cos (α-β)
   However, r is the distance between the centers of the central core and the outer peripheral core, and α is an angle representing the position of the outer peripheral core in the cross section of the multi-core optical fiber.
3. The multi-core optical fiber is given a known torsion, and when the analyzer calculates the position coordinates, the torsional strain occurring in the multi-core optical fiber and the known torsion. To estimate the unintended torsion that occurred when arranging along a linear structure whose three-dimensional shape is unknown based on the strain due to the kinking, and to exclude the influence of the unintended twist. ,
   The shape measuring system according to claim 1.
4. Let z be the position in the longitudinal direction of the multi-core optical fiber.
   The analyzer is
   The amount of strain at the position z of each core of the multi-core optical fiber obtained from the rear Brillouin scattered light distribution when the multi-core optical fiber is arranged along a linear structure whose three-dimensional shape is unknown, and the above-mentioned The difference from the strain amount of the position z of each core of the multi-core optical fiber obtained from the rear Brillouin scattered light distribution when the multi-core optical fiber is arranged along a linear structure whose three-dimensional shape is known. Calculating the differential distortion at a certain position z,
   To calculate _{the bending strain ε bending, i} of each of the outer peripheral cores by subtracting the differential strain of the central core from the differential strain of each of the outer peripheral cores.
   Using the relational expression (2) excluding the influence of the unintended twist, the curvature κ and the bending angle β at the position z of the multi-core optical fiber are calculated from the _{bending strain ε bending, i for each outer core.} , And, using the Frenet-Serret formula, calculate the position coordinates in the three-dimensional space of the linear structure whose three-dimensional shape is unknown from the curvature κ at the position z and the bending angle β.
   3. The shape measuring system according to claim 3.
   

   

   However, r is the distance between the centers of the central core and the outer peripheral core, k ₁ is the twist correction coefficient represented by the equation (3), ν is the Poisson's ratio of the multi-core optical fiber, and a _i is the core i. The initial angle of, ω _i is the angle representing the position of the outer peripheral core in the cross section at the position z of the multi-core optical fiber represented by the equation (4), p is the spin rate of the outer peripheral core, and ε _twisting is the multi-core light. The torsional strain generated at the position z of the fiber, φ (z) is the specific torsion angle at the position z of the multi-core optical fiber represented by the equation (5), and k ₂ is the equation (6). It is a correction coefficient of twist represented by.
   

   

   

   

   
5. The shape measuring system according to claim 4, wherein the analysis device calculates the spin rate p of the outer peripheral core from periodic fluctuations _{of bending strain ε bending and i of each of the outer peripheral cores.}
6. The measurement system according to any one of claims 1 to 5, wherein the multi-core optical fiber has 3 outer peripheral cores and a clad diameter of 375 μm or more.
7. The measuring system according to any one of claims 1 to 6, wherein the multi-core optical fiber has a center-to-center distance between the central core and the outer peripheral core of 120 μm or more.
   
8. Arranging a central core arranged in the center of the cross section and a multi-core optical fiber having three or more outer peripheral cores arranged concentrically at equal intervals outside the central core along the linear structure.
   Measuring the rear Brillouin scattered light distribution in the propagation direction of each core of the multi-core optical fiber, and knowing the multi-core optical fiber and the three-dimensional shape arranged along a linear structure whose three-dimensional shape is unknown. To calculate the position coordinates in the three-dimensional space of the linear structure whose three-dimensional shape is unknown from the rear Brillouin scattered light distribution of the multi-core optical fiber arranged along a certain linear structure.
   Shape measurement method.
9. When calculating the position coordinates in the three-dimensional space of the linear structure whose three-dimensional shape is unknown, the position in the longitudinal direction of the multi-core optical fiber is defined as z.
   The amount of strain at the position z of each core of the multi-core optical fiber obtained from the rear Brillouin scattered light distribution when the multi-core optical fiber is arranged along a linear structure whose three-dimensional shape is unknown, and the above-mentioned The difference from the strain amount of the position z of each core of the multi-core optical fiber obtained from the rear Brillouin scattered light distribution when the multi-core optical fiber is arranged along a linear structure whose three-dimensional shape is known. Calculating the differential distortion at a certain position z,
   To calculate the bending strain ε of each of the outer peripheral cores by subtracting the differential strain of the central core from the differential strain of each of the outer peripheral cores.
   Using the relational expression (1), calculate the curvature κ and bending angle β at the position z of the multi-core optical fiber from the bending strain ε for each outer core, and using the Frenet-Serret formula, the curvature at the position z. To calculate the position coordinates in the three-dimensional space of the linear structure whose three-dimensional shape is unknown from κ and the bending angle β.
   8. The shape measuring method according to claim 8.
   [Relational formula (1)]
   ε ＝ r ・ κ ・ cos (α-β)
   However, r is the distance between the centers of the central core and the outer peripheral core, and α is an angle representing the position of the outer peripheral core in the cross section of the multi-core optical fiber.
10. The multi-core optical fiber is given a known torsion, and when the position coordinates are calculated, the torsional strain generated in the multi-core optical fiber and the strain due to the known torsion are applied. To estimate the unintended twist that occurred when arranging along a linear structure whose three-dimensional shape is unknown based on the above, and to exclude the influence of the unintended twist.
    The shape measuring method according to claim 8.
11. When calculating the position coordinates in the three-dimensional space of the linear structure whose three-dimensional shape is unknown, the position in the longitudinal direction of the multi-core optical fiber is defined as z.
    The amount of strain at the position z of each core of the multi-core optical fiber obtained from the rear Brillouin scattered light distribution when the multi-core optical fiber is arranged along a linear structure whose three-dimensional shape is unknown, and the above-mentioned The difference from the strain amount of the position z of each core of the multi-core optical fiber obtained from the rear Brillouin scattered light distribution when the multi-core optical fiber is arranged along a linear structure whose three-dimensional shape is known. Calculating the differential distortion at a certain position z,
    To calculate _{the bending strain ε bending, i} of each of the outer peripheral cores by subtracting the differential strain of the central core from the differential strain of each of the outer peripheral cores.
    Using the relational expression (2) excluding the influence of the unintended twist, the curvature κ and the bending angle β at the position z of the multi-core optical fiber are calculated from the _{bending strain ε bending, i for each outer core.} , And, using the Frenet-Serret formula, calculate the position coordinates in the three-dimensional space of the linear structure whose three-dimensional shape is unknown from the curvature κ at the position z and the bending angle β.
    10. The shape measuring method according to claim 10.
    

    

    However, r is the distance between the centers of the central core and the outer peripheral core, k ₁ is the twist correction coefficient represented by the equation (3), ν is the Poisson's ratio of the multi-core optical fiber, and a _i is the core i. The initial angle of, ω _i is the angle representing the position of the outer peripheral core in the cross section at the position z of the multi-core optical fiber represented by the equation (4), p is the spin rate of the outer peripheral core, and ε _twisting is the multi-core light. The torsional strain generated at the position z of the fiber, φ (z) is the specific torsion angle at the position z of the multi-core optical fiber represented by the equation (5), and k ₂ is the equation (6). It is a correction coefficient of twist represented by.
    

    

    

    

    
12. The shape measuring method according to claim 11, wherein the spin rate p of the outer peripheral core is calculated from periodic fluctuations _{of bending strain ε bending and i} of each of the outer peripheral cores.
13. The shape measuring method according to any one of claims 8 to 12, wherein the multi-core optical fiber has 3 outer peripheral cores and a clad diameter of 375 μm or more.
14. The shape measuring method according to any one of claims 8 to 13, wherein the multi-core optical fiber has a center-to-center distance between the central core and the outer peripheral core of 120 μm or more.

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